A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
A New Index Calculus Algorithm with Complexity $$L(1/4+o(1))$$ in Small Characteristic
复制标题
DOI：
10.1007/978-3-662-43414-7_18
复制
发表时间：
2013-08
期刊：
影响因子：
--
通讯作者：
A. Joux
中科院分区：
文献类型：
--
作者：
A. Joux
本文提出了一种新的小特征离散时间序列的算法。该算法是基于指数演算，并包括两个新的贡献。第一种是一种新的方法，用于产生小光滑基元素之间的乘法关系。第二个是一个新的下降策略，允许我们表示的对数的任意有限域元素的元素的对数从光滑基。对于一个小的特征有限域的大小，该算法实现了启发式的复杂性出于技术原因，除非已经是一个复合的因素的权利的大小，这是通过嵌入在一个小的扩展与。
In this paper, we describe a new algorithm for discrete logarithms in small characteristic. This algorithm is based on index calculus and includes two new contributions. The first is a new method for generating multiplicative relations among elements of a small smoothness basis. The second is a new descent strategy that allows us to express the logarithm of an arbitrary finite field element in terms of the logarithm of elements from the smoothness basis. For a small characteristic finite field of size, this algorithm achieves heuristic complexityFor technical reasons, unlessis already a composite with factors of the right size, this is done by embeddingin a small extensionwith.